England emerged from the tension at an expectant national stadium to secure their passage to the World Cup finals, and Roy Hodgson said the chance to lead his side to the tournament in Brazil represented the pinnacle of his 37-year managerial career.

Wayne Rooney, with his seventh goal in six qualifying ties, and the captain Steven Gerrard scored in each half to deflate Poland and ensure England finished above Ukraine, 8-0 winners in San Marino, to win Group H.

Hodgson was thrilled by his team's fluent attacking football and their maturity in dealing with a difficult occasion, and claimed England had given themselves "a chance" of succeeding at the 2014 tournament, even if he was quick to put that prospect in proper context.

"If you want to win the lottery, buy a lottery ticket, and we have our ticket," he said, albeit that would leave England's chances of winning the World Cup at around 14,000,000 to one. "We've got a chance. I'm greatly satisfied. I think this will [top the lot in his career]. The only reason I'm cautious is I don't want to denigrate my other achievements, or for people in Switzerland to think I wasn't very proud of reaching the World Cup in 1994 or the Euros in 1996 after so many years. That was a pretty good achievement.

"But I'm English. As an Englishman, this means a little bit more.

"It means an awful lot. There'll be a lot of pressure on us in Brazil but this team is growing and accepting that pressure. The blend between the senior and young players looks good. We'll use the next six or seven months to reflect on the tournament.

"The important thing this evening was to do the job. It sounded easy: two home matches, against Montenegro and Poland, win them and no problems. But anyone involved in football knows it's not as easy as all that. The important thing for us is to keep working at our game."

Gerrard, whose late goal settled the nerves after Robert Lewandowski had spurned chances to open the scoring and later haul Poland level, dedicated the victory "to the supporters, who can go and get themselves booked for Brazil".

"It's a good time for England," said Rooney, who had headed the team into the lead just before half-time having shed his protective head band. "I think that was the first time I've headed the ball without that on. We fully deserved to win. We've always remained positive, we've had great focus and belief in ourselves. There's a great blend between the young players and the more experienced lads, like Steven and Frank [Lampard]. But, tonight, a big part was being patient."

Their nerves were tested whenever Poland sprang forward on the counterattack while Wojciech Szczesny excelled in the visitors' goal.

"My emotions are still churning around inside me," Hodgson said. "I died a thousand deaths every time they crossed the halfway line, which is what you do, and our second goal took about 10 years off [assistant manager] Ray Lewington's and my lives. And I need it more than Ray.

"We'd played some sensational football in the first half, some of it quite spectacular. We dug in for a spell in the second half, which we did very well. We couldn't relax because, for a team with nothing to play for, Poland showed a lot of heart and fight.

"We came through and it's job done. It was appropriate that Steven scored the second goal because if anyone's played a captain's innings for the team, it's him. We're very happy and looking forward to going to Brazil, something the whole nation wanted.

"And I have great trust in my players that they will not let us down there. We've been working together for 18 months and the way we play has changed. We're getting better all the time and hopefully will get better still. The players really are a group and they trust each other."

England's progress in the last week, winning nerve-shredding games, has been clear with players like Andros Townsend thriving in unfamiliar surroundings. Their progress was recognised by the Poland manager, Waldemar Fornalik, who had seen the English splutter to an unconvincing 1-1 draw in Warsaw a year ago. "England are getting stronger and stronger," he said. "Compare how England played against us last year, or against Montenegro, and now. They look better every match they play and they will always be among the contenders for the title."

"We've found a winger in Andros who looks as though he's been playing [international football] all his life," Hodgson said. "He's going to be under a lot of pressure now but he's a level-headed young man and he'll deal with it.

"I fancy there'll be another 15 players joining us and meriting selection on the basis of what they've done or are capable of doing, so it'll be a tough job to pick only 23. But I'm not going to contemplate that for a few months. The record's good – we're unbeaten in qualifying – and we've done the job, so we can be proud of that achievement and just look forward to getting our reward: playing in Brazil."